The idea of using neutrinos from GRBs to explore quantum-gravity-induced
Lorentz violation was first proposed by Jacob and Piran in
2007 [1]}. Amelino-Camelia and collaborators found the
associations between GRBs and nine IceCube shower neutrino events
with the energies between 60 to 500 TeV [2]}, [3]}, and
found roughly compatible energy-dependent speed variation features
between GRB neutrinos and GRB photons. In our former work [4]}, we found that all four IceCube events
of PeV scale neutrinos
can be associated with GRBs.
Furthermore, we also suggested different propagation properties
between neutrinos and anti-neutrinos due to the existence of both time “delay” and “advance” events.
Such different neutrino/anti-neutrino propagation properties can be described in an effective field theory framework with \(CPT\) -odd terms of Lorentz invariance violation [5]}.
Therefore both PeV and TeV neutrino events
satisfy a same speed variation regularity
based on the assumption of an observable Lorentz violation effect
of neutrinos and anti-neutrinos.
Recently, from the associations between GRBs and near-TeV events reported by
IceCube Collaboration, it is found that 12 near-TeV northern
hemisphere track events can fall on the same line [6]}. In
this current paper, we show that another 3 or more track events above 30 TeV can
be associated with GRBs and satisfy the same regularity. Based on these
supports, the energy-dependent speed variation feature of
ultrahigh-energy neutrinos with the LV scale \(E_{\rm LV}=(6.4\pm 1.5)\times 10^{17}{\rm GeV}\) 
emergences as a more supportive regularity.
